U.S. Pat. No. 4,645,444 and British Pat. No. 1,350,496 generally disclose spinning systems of the known type in which at least one wall of the heating box is movable so that the spinning head can be clamped in position between the fixed walls and the movable wall of the vertical opening in the heating box in which the spinning head is supported. This type of spinning system produces a good transfer of heat between the heating box and the spinning head. However, this system of clamping the spinning head in position in the heating box has the disadvantage that the spinning head is normally removed only in an upward direction and the components of the heating box must be disassembled from each other in order to remove the spinning head. The spinning system disclosed in British Pat. No. 1,350,496 also has the disadvantage that the outer portions of the opening in the heating box remain open in an upward direction so that a strong heat convection or "chimney" effect is present and a substantial loss of heat occurs so that irregular temperatures in the spinning head can result.